Sofia Franchini, Lancaster University
Igusa-Todorov's discrete cluster category of type A-infinity

The Igusa-Todorov's discrete cluster category of type A-infinity can be thought as a generalization of the Holm-Jørgensen's 2-cluster category of type A-infinity. Both categories are triangulated and have 2 Calabi-Yau dimension. They can also be understood through a geometric model: their indecomposable objects can be identified as arcs of an infinity-gon. In this talk we will see the definition of Igusa-Todorov's category and the classification in combinatorial terms of the cluster-tilting subcategories, the torsion pairs, and the thick subcategories.